Electrostatic Instabilities at High Frequency in a Plasma Shock Front

New electrostatic instabilities in the plasma shock front are reported. These instabilities are driven by the electro- static field which is caused by charge separation and the parameter gradients in a plasma shock front. The linear analysis to the high frequency branch of electrostatic instabilities has been carried out and the dispersion relations are obtained numerically. There are unstable disturbing waves in both the parallel and perpendicular directions of shock propagation. The real frequencies of both unstable waves are similar to the electron electrostatic wave, and the unstable growth rate in the parallel direction is much greater than the one in the perpendicular direction. The dependence of growth rates on the electric field and parameter gradients is also presented.